Xin Xiao, Sultan Faisal, Yaseen Muhammad, Sherif El-Sayed M, Ishaq Muhammad Shoaib
College of Foreign Studies, Shandong Technology and Business University, Yantai, 264005, China.
Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology Rahimyar Khan, Pakistan.
Heliyon. 2024 Aug 2;10(16):e35693. doi: 10.1016/j.heliyon.2024.e35693. eCollection 2024 Aug 30.
This article presents the notion about Slow Invariant Manifold (SIM) and their fundamental role in model reduction techniques (MRTs) for challenges encountered in mechanical engineering within dissipative systems of chemical kinetics. Focusing on the reaction routes of complex mechanisms, we construct and compare primary approximations of the SIM through MRTs, including the Spectral Quasi Equilibrium Manifold (SQEM) and Intrinsic Low Dimensional Manifold (ILDM). These methods effectively transform high-dimensional complex problems into lower dimensions, solving them without compromising crucial information about the complex systems modified for homogeneous reactive systems. Employing the sensitivity analysis by using the MATLAB's toolbox, we present the numerical findings in a tabular format obtained through MRTs. This study provides the understanding about the accessible exploration of numerical solutions, improving insights of the complex variation within the system.
本文提出了慢不变流形（SIM）的概念及其在化学动力学耗散系统中机械工程所面临挑战的模型约简技术（MRTs）中的基本作用。聚焦于复杂反应机理的反应路径，我们通过MRTs构建并比较了SIM的主要近似，包括谱准平衡流形（SQEM）和本征低维流形（ILDM）。这些方法有效地将高维复杂问题转化为低维问题，在不损失为均相反应系统修改的复杂系统关键信息的情况下求解。利用MATLAB工具箱进行灵敏度分析，我们以表格形式呈现了通过MRTs获得的数值结果。本研究提供了对数值解可及探索的理解，增进了对系统内复杂变化的认识。
